[anonymoushn]

It contains the sentence "For any distribution, the sum of probabilities always equals 1" without the caveat that the sum is of a countable number of probabilities. It applies to every continuous distribution using the same argument, but with "the sum across all naturals" replaced with "the sum across the appropriate universe."

[Fargren]

"the sum across the appropriate universe" for Reals is an integral. An integral can go from -Infinite to Infinite and still equal 1. This is the reason, for instance, why Zeno's Paradox of movement doesn't really forbid all movement.

[anonymoushn]

This comment is more or less irrelevant. The third axiom of probability is about sums of countably many terms: http://en.wikipedia.org/wiki/Axioms_of_probability#Third_axi...